Who was first to use and invent the term?
Also spelt "doobly doo". There's a related page here tracing usage of the term back to a guy called Craig Benzine (a Youtube user).
But to my ear, "doobly doo" sounds like a familiar idiom that's much older than that, used to name something you don't know the name of.
"You know, the doobly doo ... the doobly doo for flipping eggs."
This first appears on WheezyWaiter and was popularized in part by vlogbrothers. Quoted from Urban Dictionary:
This term refers to the video description box on YouTube.
This box, which contains information about the video, links, and tags, used to be universally referred to as the "sidebar," since it often appeared beside videos, but Craig Benzine (Wheezy Waiter) started referring to it as the "doobly-doo."
Other YouTubers, such as John Green (part of the Vlogbrothers) and Dan Brown, started to also call the sidebar the "doobly-doo," using Wheezy Waiter's terminology (and crediting him in various comments and tweets). The term is now widely used on YouTube.
I noticed that the term is used in the song “Funky Monks” (1991) by the Red Hot Chili Peppers, though obviously not with the same meaning:
Virtue slipped into my shoe
No I will not misconstrue
More rockin’ more rockin’ now doobley do
Dancin’ down your avenue
The nonsensical nature of the verse makes me think it might just be a placeholder word, perhaps with a longer history as @badroit suggests.
Of course, Craig Benzine’s coinage might be completely independent.